Why can't I add pip to the version of Python that comes with Blender 2.91.2?
I had to go through several other issues to pin this down, including another question on stack Overflow, where I was not getting much help. I'll include what I can here. That'll be more than most people want to read, but if you have this problem, skim it because you might find helpful stuff in here.
The bottom line is that I was setting PYTHONPATH in .bash_profile. When I bought this current iMac, Python 2.7 was the standard on an install. At some point (and I had forgotten this), Apple changed to 3.x as the standard. That crashed some of my scripts, so I set PYTHONPATH (again, in .bash_profile) to point to all the 2.7 libraries, so my scripts would continue to look there.
I finally figured out that any 3.x version of Python was crashing on my system and 2.x was running. I thought that was probably a configuration issue and I'd have to find some config file to fix somewhere, but, all along, it was in the .bash_profile. Once I changed all the paths in there to point to 3.7 instead of 2.7, everything started working fine. Python 3 executables were working fine and even the 2.x ones were still working. (And more of my scripts than I expected worked fine under 3.x.)
Once I got that working, I wrote a batch file I can run in bash to set PYTHONPATH to point to the directories Blender uses when it runs Python in its own environment then run the Blender instance of Python. It works fine and that let me follow instructions in a number of places to use ensurepip to install pip and then to install Pillow.